Non- or semiparametric estimation and lag selection methods are proposed for three seasonal nonlinear autoregressive models of varying seasonal flexibility. All procedures are based on either local constant or local linear estimation. For the semiparametric models, after preliminary estimation of the seasonal parameters, the function estimation and lag selection are the same as nonparametric estimation and lag selection for standard models. A Monte Carlo study demonstrates good performance of all three methods. The semiparametric methods are applied to German real gross national product and UK public investment data. For these series our procedures provide evidence of nonlinear dynamics.